Spotify

2023-03-30

Adi Tewari, Anouk Seibulescu, Donald Conway, and Xiangyu Huang

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Introduction

Background

Analysis

p_hat1 p_hat2 diff
0.38 0.32 0.06

Statistical Model

The statistical model is:

\[ X_1 \mid p_1 \sim \text{Binomial}(50,p_1) \\ X_2 \mid p_2 \sim \text{Binomial}(50,p_2) \]

Confidence Interval from Simulation

SE Simmulation
0.0951949
\[(\text{point estimate}) \pm 1.96 \times (\text{standard error})\]
Point_estimate SE z Low High
0.06 0.0951949 1.959964 -0.1265785 0.2465785

Confidence Interval using formula

\[ \text{SE}(\hat{p}_1 - \hat{p}_2) = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2} } \]

se Point_estimate z Low High
0.095205 0.06 1.959964 -0.1265985 0.2465985

Hypothesis Tests for Testing Differences

Inference question
Group Explicit Songs Total Songs p_hat
Top 0-50 19 50 0.38
Top 51-100 16 50 0.32

Testing from Simulation

Statistical Model

The statistical model is:

\[ X_1 \mid p_1 \sim \text{Binomial}(50,p_1) \\ X_2 \mid p_2 \sim \text{Binomial}(50,p_2) \]

State hypotheses:

\[ H_0: p_1 = p_2 \\ H_a: p_1 \neq p_2 \] - The null hypothesis is there is no difference in the proportion of explicit songs in the Top 0-50 vs Top 51-100

Calculating a test statistic:

test_stat
0.06

Determining the null sampling distribution of the test statistic

p0
0.35

Calculating the p-value via simulation - the number of replications will be \(1,000,000\)

p value from simmulation
0.600682

Normal approximation for p-value

\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{\text{SE}} \]

\[ \text{SE}(\hat{p}_1 - \hat{p}_2) = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2} } \]

z statistic
0.6289709
p value from z statistic
0.5293681

Graphical representation

Discussion

Reference

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  1. Is there an Explicit Content filter? - The Spotify Commun. . .. (2023, January 28). https://community.spotify.com/t5/FAQs/Is-there-an-Explicit-Content-filter/ta-p/4631272↩︎

  2. Spotify - About Spotify. (2023, March 9). Spotify. https://newsroom.spotify.com/company-info/↩︎

  3. Trust, G. (2014, September 7). Billboard. Billboard. https://www.billboard.com/pro/ask-billboard-how-does-the-hot-100-work/↩︎

  4. What Is The Billboard Hot 100? (2023, January 2). Edmsauce. Retrieved April 10, 2023, from https://www.edmsauce.com/what-is-the-billboard-hot-100/↩︎